psm12se wrote:How many three-digit odd integers less than 500 are there so that all the digits are not distinct?
A. 56
B. 88
C. 144
D. 200
E. 250
Integers with all 3 digits NOT distinct = total number of integers - integers with all 3 digits distinct.
Total number of integers:
To count consecutive integers:
Number of integers = biggest - smallest + 1.
Thus, from 100 to 499, inclusive:
Number of integers = 499 - 100 + 1 = 400.
Integers with all 3 digits distinct:
Number of options for the hundreds digit = 4. (1, 2, 3 or 4).
Number of options for the tens digit = 9. (Any digit 0-9 but the digit already used.)
Number of options for the units digit = 8. (Any digit 0-9 but the 2 digits already used.)
To combine these options, we multiply:
4*9*8 = 288.
Thus, from 100 to 499, inclusive:
Number of integers with all 3 digits NOT distinct = 400-288 = 112.
Of these 112 integers, exactly HALF will be odd:
112/2 = 56.
The correct answer is
A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
